Rapid simulation of spatial epidemics: A spectral method

Abstract

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or subpopulations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational e ciency of spatial simulations. We demonstrate the e ciency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel. Highlights• Kernel-based spatial transmission models are computationally expensive for large population sizes.• We present an e cient and accurate alternative simulation methodology (dubbed FSR simulation) based upon a spectral representation of the infection rate.• FSR simulation also permits the accelerated likelihood calculation for more e cient parameter inference.• Using FSR simulation it was possible to perform detailed outbreak forecasting for a generic cattle infection at the continental-scale.

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

“…Applied epidemiological modeling is challenged by limited data, either because information is withheld due to confidentiality concerns or because the data has not been collected. In the absence of exact information regarding premises demography and contact patterns, modelers have to extrapolate from available information and make assumptions about spatial distributions [19,22,26]. Here we considered potential for FMD transmission within the U.S. cattle industry, where publicly available demography data are aggregated to the county level.…”

“…The most comprehensive inventory of U.S. livestock demography is provided by the National Agriculture Statistics Service (NASS), which conducts surveys of the livestock and poultry industries and provides demographic data describing animal inventory and number of premises aggregated at the county level. Thus, there is an absence of detailed information about the spatial distribution of the premises, prompting livestock disease modelers to assume either randomly distributed premises [19] or mass-action mixing [20] within counties. However, there may be problems associated with such assumptions.…”

“…To answer this, we used spatial distributions of premises as predicted by FLAPS, and landscapes where the premises' locations were randomized within their respective counties, together with three implementations of previously published FMD models. The models all shared the same premises-level, kernel-based structure that was first developed for the 2001 FMD outbreak in the UK [4] and are referred to by the first name of the original publications, Brand [19], Hayama [3] and Tildesley [24]. Using these models, we performed two different analyses to evaluate the importance that detailed premises locations would have for the dynamics of a potential FMD outbreak within the U.S cattle population.…”

Computational methods for risk assessment in ecological and epidemiological contexts

“…Other compartments can also be added such as en exposed class (E) for infections with a latency period before the onset of infectiousness. The epidemic model used in Papers III and IV is a stochastic, spatially explicit, discrete-time SEIR model; a type of model that is well suited for the modeling of FMD and one that has been a popular choice ever since the 2001 outbreak in the UK (Keeling, Woolhouse, Shaw, et al, 2001;Keeling, Woolhouse, May, et al, 2003;Keeling, 2005;Tildesley and Keeling, 2008;Boender et al, 2010;Rorres et al, 2011;Hayama et al, 2013;Brand, Tildesley, et al, 2015). In this type of model, a premises is commonly regarded as a single infective unit in the perspective of the SEIR-framework.…”

“…Modeling the spread of disease among livestock (Papers III and IV) in some cases to achieve larger outbreaks. The sources for the kernel functions are, Brand, Tildesley, et al (2015), Hayama et al (2013), Buhnerkempe et al (2014). After infection has occurred, the premises enters the exposed class for a fixed latency period that varied between two and five days depending on the kernel model, after which the infected premises entered the infectious compartment.…”